Orbital formulas

[7499275]

Hey guys, just wanted some help or thoughts on this.

I am currently a junior (starting in August) in high school. Last year I was recommended for advanced Juinor math. I asked my math teacher who recommended me to teach me some things that are apparently calculus.

This is the formula for DeltaV. I wanted to expand my knowledge of orbital physics and formulas so I could do KSP math by hand on paper. In a really nice long method he said no, I of course asked why? He claimed basically that it would take a lot of time to just jump into things like a constant which is the little S looking thing (right?) He said he would give me extra tutorial if I still wanted after my Juinor year (year I take calculus)

I have no idea what several of those other signs mean in the formula, I guess I am kinda asking for someone to show some pity upon me and maybe try to help me learn to do some formulas by hand.

[PakledHostage]

He said he would give me extra tutorial if I still wanted after my Juinor year (year I take calculus)

I have no idea what several of those other signs mean in the formula, I guess I am kinda asking for someone to show some pity upon me and maybe try to help me learn to do some formulas by hand.

I would agree with him. I worked as a TA and a tutor for first and second year calculus students while I was studying engineering at university and I encountered far too many students who didn't have a good enough foundation in the basics of mathematics to succeed at calculus. Calculus isn't "plug and chug". You need solid algebra skills and a good understanding of concepts like limits and differentiation before you start with integration. It sounds like you're pretty smart and you'll progress quicker than most students, but do yourself a favor and start at the bottom and work your way up. Wax on, wax off, to use a cliche...

[7499275]

I would agree with him. I worked as a TA and a tutor for first and second year calculus students while I was studying engineering at university and I encountered far too many students who didn't have a good enough foundation in the basics of mathematics to succeed at calculus. Calculus isn't "plug and chug". You need solid algebra skills and a good understanding of concepts like limits and differentiation before you start with integration. It sounds like you're pretty smart and you'll progress quicker than most students, but do yourself a favor and start at the bottom and work your way up. Wax on, wax off, to use a cliche...

I guess this may have been a dumb thing to post because of that. You do have a good point I do realize that math is a building block process, I just do get impatient sometimes as for school to start so I could begin calculus at the least.

[PakledHostage]

I guess this may have been a dumb thing to post because of that.

Well if all you're after are some equations to use in KSP, then why not start with something like Basics of Space Flight: Orbital Mechanics and leave the derivations of the equations used on that website until after you've done enough math and physics for it to mean something?

[7499275]

Well if all you're after are some equations to use in KSP, then why not start with something like Basics of Space Flight: Orbital Mechanics and leave the derivations of the equations used on that website until after you've done enough math and physics for it to mean something?

Bookmarked, thank you for that link. I've only skimmed it a little bit as its late, but will read more in depth on it tomorrow, I will admit, I know some of that stuff but not nearly as much as I thought lol thanks again.

[cpast]

I also agree your teacher - while calculus *can* be done mechanically, you aren't actually learning anything by doing so. Also, for this specific case (the delta-V formula), you don't need calculus at all - the more standard way to calculate it is: delta-V = v_e * ln(m_wet / m_dry), where v_e is effective exhaust velocity (and is equal to g * I_sp; g is the gravity at sea level on Earth, and applies in space because of what I_sp represents, which is impulse per unit *weight* of propelland at sea level on Earth; I_sp is, well, that, and is a parameter of the engine; m_wet is mass of rocket with propellant; m_dry is mass of the rocket without propellant). This is true for most equations you have to deal with in KSP: you can, in fact, calculate things perfectly well without any calculus. Now, learning calculus is nice, and lets you see actually *why* delta-V works the way it does. But if you just learn plug-and-chug, you still aren't gaining any insight - there's no point rederiving the delta-V formula if you don't understand the meaning behind what you're doing.

[K^2]

Don't consider this a substitute for learning Calculus (and subsequently Analysis) properly, but as a quick patch, and to get you started, watch

. It will give you some idea on what's going on.

To derive the actual rocket formula, you need to know a few more things, but the important bit is that instead of working with acceleration/forces and integrating over time, you consider how the momentum changes with respect to fuel consumed (specific impulse) and integrate over mass of the ship. You do this right and you will get Tsiolkovsky's rocket formula.

A lot of orbital mechanics can be learned without knowing Calculus, though. You'd be missing out, but if you understand Conservation of Energy and Conservation of Angular Momentum, you are off to a good start.

the more standard way to calculate it is: delta-V = v_e * ln(m_wet / m_dry)

That formula is derived from equation he wrote down, though. You just have to do a change of variable (|T|dt = - g I_SP dm) and then integrating from m_wet to m_dry.

Edited July 3, 2014 by K^2

[cpast]

That formula is derived from equation he wrote down, though. You just have to do a change of variable (|T|dt = - g I_SP dm) and then integrating from m_wet to m_dry.

I know; I'm perfectly able to derive it myself (and in fact, the first time I learned the rocket equation was in a physics class where it was derived as an example). My point was that knowing the derivation only helps if he *understands* it, which requires more than a quick study of calculus. If he doesn't understand the derivation, there's no point doing a bunch of symbol-manipulation to go from the original to the one people actually use; the original adds complexity for little value (it's legitimately useful if I_sp varies, but then you're likely past the point where you can do the problem without some understanding of what you're doing).